The stationary wave produced on a string is represented by the equation $y=5\cos (\pi x/3)\sin 40\pi t$ where x and y are in cm and t is in seconds. The distance between consecutive nodes is :

1. 5 cm

2. π cm

3. 3 cm

4. 40 cm

The tension in a piano wire is 10N. What should be the tension in the wire to produce a note of double the frequency :

(1) 5 N

(2) 20 N

(3) 40 N

(4) 80 N

Three similar wires of frequency n₁, n₂ and n₃ are joined to make one wire. Its frequency will be :

(1) $n=n_1+n_2+n_3$

(2) $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$

(3) $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$

(4) $\frac{1}{n^1}=\frac{1}{n_1^2}+\frac{1}{n_2^2}+\frac{1}{n_3^2}$

A string is rigidly tied at two ends and its equation of vibration is given by $y=\left(\cos 2\mathrm{\pi }t \right)\left(\sin 2\mathrm{\pi }x\right)$Then minimum length of the string is :

1. 1 m

2. $\frac{1}{2}m$

3. 5 m

4. 2π m

In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. The tension of the string remaining constant the frequency of the second tuning fork is :

(1) 163.84 Hz

(2) 400 Hz

(3) 320 Hz

(4) 204.8 Hz

An empty vessel is getting filled with water, then the frequency of vibration of the air column in the vessel 

(1) Remains the same

(2) Decreases

(3) Increases

(4) First increases then decrease

A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude ${\rho }_0$ inside the tube. If the atmospheric pressure is ${\rho }_A$ , then the ratio of maximum and minimum pressure at the closed end of the tube will be :

1. $\frac{({\rho }_A+{\rho }_0)}{({\rho }_A-{\rho }_0)}$

2. $\frac{({\rho }_A+2{\rho }_0)}{({\rho }_A-2{\rho }_0)}$

3. $\frac{{\rho }_A}{{\rho }_A}$

4. $\frac{\left({\rho }_A+\frac{1}{2}{\rho }_0\right)}{\left({\rho }_A-\frac{1}{2}{\rho }_0\right)}$

An open pipe of length l vibrates in the fundamental mode. The pressure variation is maximum at :

(1) 1/4 from ends

(2) The middle of the pipe

(3) The ends of the pipe

(4) At 1/8 from ends of pipe middle of the pipe

In a closed organ pipe, the frequency of the fundamental note is 50 Hz. The note of which of the following frequencies will not be emitted by it :

(1) 50 Hz

(2) 100 Hz

(3) 150 Hz

(4) None of the above

The frequency of a whistle of an engine is 600 cycles/sec is moving with the speed of 30 m/sec towards an observer. The apparent frequency will be (velocity of sound = 330 m/s) [MP PMT 1989]

(1) 600 cps

(2) 660 cps

(3) 990 cps

(4) 330 cps